Mathematical Monday: Platonic Solids

Quick, D&D players--Which of these is most different from the others: the d4, d6, d8, d10, d12, or d20? (For those unfamiliar with such tabletop games, those are dice with the specified number of sides.) The answer is the d10. Why? It's the only one that isn't a Platonic solid!*

A Platonic solid is essentially a regular convex polyhedron. Simply put, polyhedron = 3D shape, convex = has no indents on the outside that could be used to collect water, and regular = same all around (for example, regular polygons--2D shapes--have all side lengths and all angles the same, as in a square or the shape of a stop sign). More specifically, the faces of a Platonic solid are all identical, regular convex polygons, with the same number of faces meeting at each vertex. Thus, all of its edges, faces, and angles are identical.

While there are an infinite number of regular polygons (they start to look more and more like circles as they get more sides, but still), there are exactly five Platonic solids. They all properly have "regular" in front of their names listed below, but usually when the following names are used alone, the regular version of the shape is implied.



Tetrahedron (the d4)
4 triangular faces, 4 vertices, 6 edges
The tetrahedral shape is common in chemistry, formed when one atom shares covalent bonds with four other atoms (with a bunch of caveats that we won't get into here), as in methane, CH4. The hydrogen atoms arrange themselves around the carbon atom such that they would be at the four vertices of a tetrahedron.

Hexahedron, aka Cube (the d6, classic die)
6 square faces, 8 vertices, 12 edges
Everyone's familiar with the cube--it's so common that it has its own special name in addition to the name that specifies its number of sides. The volume of a cube is easy to compute--just take the length of its edge and, well, cube it! Thanks to our perception of 3D space, the cube is intimately tied to how we think about volume and even the term for raising something to the 3rd power.

Octahedron (the d8)
8 triangular faces, 6 vertices, 12 edges
Diamond and fluorite crystals are often octahedrons in nature.

Dodecahedron (the d12)
12 pentagonal faces, 20 vertices, 30 edges
Some quasicrystals, such as Holonium-Magnesium-Zinc crystals, can be dodecahedra.

Icosahedron (the d20)
20 triangular faces, 12 vertices, 30 edges
Viruses often have icosahedral or near icosahedral shapes. This is likely due to the fact that it's a vaguely spherical shape (a convenient shape for maximizing volume for minimal surface area and looking the same from many angles) that can be constructed from a bunch of identical pieces, so it's not too complicated to code for the construction of new viruses within a cell.

These shapes have been known since ancient times. The Platonic solids have been found in carved stone balls made by Scotland's neolithic people from before 1300 B.C. Plato c. 360 B.C. associated each of the classical elements (earth, air, water, fire) with one of the solids, and his contemporary Theaetetus may be responsible for the proof that only five such solids exist. These people recognized the uniqueness of these polyhedra, and hopefully you have a new appreciation for them as well.


* If you answered the d4, because it's the only one that lands with a vertex at the top instead of a face looking up, then I suppose that's a practical answer as well. But it kind of messes with my intro.

Smithsonian Art of Video Games Exhibit--Vote!

Whatever some close-minded people might think, the Smithsonian American Art Museum believes that video games can be art. They are planning an Art of Video Games Exhibit that will run from March 16 - September 30, 2012. From the description on the museum website:

Video games use images, actions, and player participation to tell stories and engage their audiences. In the same way as film, animation, and performance, they can be considered a compelling and influential form of narrative art.

The Art of Video Games is one of the first exhibitions to explore the forty-year evolution of video games as an artistic medium, with a focus on striking visual effects and the creative use of new technologies.

I am very excited by this exhibit and the recognition it will bring to deserving games. What's more, right now we can vote on which games we think should be displayed in the exhibit!



The games are divided into five eras. Start! (1970s - early 1980s) has games from Atari VCS, ColecoVision, and Mattel Intellivision. I was pretty little when we got my cousin's Atari as a hand-me-down, but I remember days of Pac-Man, Missile Command, Space Invaders, and E.T. the Extra-Terrestrial. 8-Bit (1983-1989) has games from Commodore 64, NES, and SEGA Master System. I remember trying Duck Hunt at a friend's house, but I mostly missed this era. Bit Wars! (1989-1994) has games from SEGA Genesis, which I played a lot of back in the day though sadly none of the games listed are games that my family owned (I guess we didn't have very artistic tastes), and the Super Nintendo. Transition (1995-2002) is getting a little more towards my true gaming era, with sections for DOS/Windows, Nintendo 64, SEGA Dreamcast, Saturn, and Sony PlayStation. My old favorites Baldur's Gate II: Shadows of Amn (my all-time favorite, really), Diablo II, and Final Fantasy Tactics are there, plus others that I remember fondly (but was less familiar with myself), such as Super Mario 64, GoldenEye 007, and StarCraft. Lastly, Next Generation (2003-current) has games from Xbox, Xbox 360, modern Windows, Nintendo GameCube, Wii, PlayStation 2, and PlayStation 3. Mass Effect 2, Star Wars: Knights of the Old Republic, Dragon Age: Origins, and Portal can be found here, with plenty of other games that are well loved today: World of Warcraft, Fallout 3, Minecraft, Epic Mickey, Super Mario Galaxy 2, Flower, Halo 2 and 3, BioShock, Fable, Oblivion, Half Life 2, and more (whew!).

Some games, particularly the newer ones with (what are today considered) advanced graphics, are easier to recognize as artistic in an aesthetically beautiful sense. Others are artful in the stories they tell, their use of technology to tell those stories, and the ways they interact with the audience. There are many worthy games on the list. So go vote for your favorites! Voting closes April 7, 2011.
http://www.artofvideogames.org/

Mathematical Monday: Bee Genetics

Having loved math since an early age (I was a big fan of Square One on PBS), I've enjoyed reading Rosalind's Mathematical Monday posts over at Girls Are Geeks. Her post today on family genetics got me thinking about one of my favorite bits of math-related genetic trivia, inspiring me to write a Mathematical Monday post of my own.

Bees, and other members of the family Hymenoptera (e.g. ants, wasps, hornets), have a peculiar genetic characteristic in that the females are diploid, or have two sets of chromosomes, while the males are haploid, or have one set of chromosomes. Humans, and most of the animals that we are familiar with, are all diploid; we get one set of chromosomes from our mother, and one set from our father. In Hymenoptera, a female gets one set of chromosomes from her mother and one set from her father, but a male only gets one set from his mother and has no father. Basically, an unfertilized egg develops into a male while a fertilized egg will become a female. This fascinating genetic trait actually helps explain the colonial behavior observed in many Hymenoptera, including honeybees. Why? The answer is in the math.

Consider humans. A mother has two sets of chromosomes--two sets of each gene. She mates with a man who also has two sets of each gene (with the odd exception of the Y chromosome vs. X chromosome, but we need not get into that complication for these purposes). Her offspring will receive 50% of their genes from her, and 50% from her mate. So the parents will share 50% of their genes with each of their children. What's more, these offspring in turn share on average 50% of their genes with each other. It's a little harder to see this, but imagine that one offspring has already been born, with one set of genes coming from his mother and another set coming from his father. Since the mother has two sets of genes to give, as does the father, the chance that a second offspring will have the same version of any particular gene that the first offspring has is 50%: 50% chance of getting the same hair color gene from the mother (since she has two), 50% chance of getting the same hair color gene from the father (since he has two), 50% chance of getting the same maternal eye color gene, etc. This can be put in a sort of rough formula as follows, where we take this idea that on average one out of every two genes from the mother (and father) will be the same between siblings.
(1 gene similar with sibling/out of every 2 genes from mother) * 50% of genes come from mother + (1 gene similar with sibling/out of every 2 genes from father) * 50% of genes come from father = 25% + 25 % = 50% genes similar with sibling

Now consider a honeybee (I focus on them because they were the specialty of my college biology professor). A queen bee producing female offspring is, like humans, 50% related to her daughters; the daughters get 50% of their genes from the mother and 50% of their genes from their father. However, while a honeybee has a 50% chance of sharing any particular maternal gene with one of her sisters, because the father only has one set of genes, she has a 100% chance of sharing every paternal gene with her sisters. To make an analogous formula,
(1 gene similar with sister/out of every 2 genes from mother) * 50% of genes come from mother + (1 gene similar with sister/out of every 1 gene from father) * 50% of genes come from father = 25% + 50% = 75% genes similar with sisters
Note: I ignore the males because they are kind of a lost cause--in honeybee colonies, they can't be workers, and their only role is to mate, then die ;)

So a honeybee shares more in common genetically with her sisters (75% on average) than she would with her offspring (50%). Therefore, a female honeybee's genes are actually better propagated by her having more sisters than by having children of her own. This may explain why honeybees and other members of Hymenoptera colonize, letting one "queen" (really, just a baby-making sucker) produce children while all the sisters take care of each other and the hive. This colony behavior may have been more successful in propagating genes than other tactics, and so the behavior was successfully passed on throughout the generations.

The best Valentine, not the best Valentine's Day

Some of you may recall that I had my first real Valentine's Day last year, which was wonderful. Last year, Valentine's Day fell on a Sunday, so the Housemate and I had a leisurely breakfast that he cooked, drove around the island in perfect Hawaii weather, then enjoyed a delicious meal at what is possibly the best restaurant I've ever been to.

This year's Valentine's Day was less than ideal. First of all, it fell on a Monday, which is generally the worst day of the week. We had cereal for breakfast, though I did open up a passion fruit I had been letting ripen for a while and it was sweet and tart and delicious. Then I had to go into school for a morning class. Don't tell my advisor, but I spent my early afternoon drawing my boyfriend a Valentine (I need some colored pencils or something; I did this entirely with a black pen). Front, inside left, and back:

Because he just came back from Antarctica, and he studies viruses, see? He complimented me on the accuracy of my Adelie penguins, so I was pretty pleased with myself.

We left school around 4pm, had a nap, exchanged a couple gifts, and just had a very nice late afternoon/early evening together. Then we got ready for our dinner reservation. In spite of it being a Monday and a work day, Valentine's Day had been pretty nice so far.

Our reservation was at 8:30. We got there at 8:30. It was a zoo. For 5-10 minutes, there was no clear host or hostess. We finally figured out whom to ask about our reservation, but when we told her we were there for our reservation, she just asked our name, how many people, and wrote it on a list. She was doing the same thing for people who did and didn't have reservations. And I even noticed her seating one pair whose name was after ours on the list. It was hugely unorganized, and this lady was also acting as cashier and waitress, so she was running around crazy. I was annoyed, but patient. As long as the dinner was good, it would be worth it.

We finally got seated shortly after 9, as four or more tables cleared up suddenly at the same time. The food was pretty good--not as good as Roy's last year, but nice. Corn chowder as the soup course, Laotian spring rolls and a salad as an appetizer, and fisherman's pot pie for an entree (seafood and vegetables and lots of pleasantly spicy gravy spooned out between two layers of puff pastry). But some time around the entree course, my stomach started feeling pretty uncomfortable. Before dessert, I had to excuse myself to the ladies' room...

The desserts were really why I'd chosen this restaurant in the first place, as they have a lovely selection of beautiful French pastries. I'd been there once before for dessert and their hot chocolate, which was rich and made with real chocolate--the best I'd had since Paris. So when I got back, we ordered our pastries (I got the chocolate macaroon one, and the Housemate got the banana haupia one) and one hot chocolate. But when the hot chocolate came, it was paler than coffee ice cream. I sent it back saying it wasn't chocolaty enough, and the waitress brought it back later, this time a dark brown, but it still just tasted like it was made with normal cocoa powder. I was really disappointed since I'd raved about the rich chocolate to the Housemate when we ordered it. Not sure what went wrong there. The desserts were delicious, but I could hardly eat them because my stomach was feeling unstable. So I had mine put in a box, and we went home. At least I can look forward to eating it tonight.

It was 11:30 by this point (dinner took a long time), so we got home and got ready for bed. But after I brushed my teeth, I threw up. Everything. It would have been a miserable end to a miserable evening if not for my boyfriend. He was very sweet and comforting the whole evening, the perfect company for Valentine's Day. And when I got in bed he gave me a back massage. Yes, things could have been better, but they could have been much worse. I was happy.

The Housemate is back!

Just an update -

I got back from my research cruise on Thursday afternoon. It was amazing, I had a lot of fun, we saw some beautiful sights, and I ate a ton of really delicious and impressive food. I will definitely be writing some posts on the cruise in the near future, once I find time to go through all the photos I took.

The Housemate finally came back from Antarctica on Friday afternoon, having left so long ago on October 26. I drove to the airport to pick him up, and I have to say that it was actually a little weird when I saw him--like my brain didn't quite believe he was really there, and not just video chatting with me again. Also I had asked him to grow out his beard so I could see and feel it when he came home, so when he climbed in the car I wasn't sure how to go about kissing him. Too. Much. Hair. But that initial strangeness aside, I am now very happy to have him back. And the beard is gone.

In addition to writing about my cruise, I need to catch up on everyone's blogs because I didn't read too many posts when I was on the boat. But first I need to catch up on school work. I did a little homework on the ship though not enough, and I have lectures I missed to go through the notes for and a lot of reading to do. So things will get back to normal at some point, but the next week or so will be pretty busy. I promise I'll catch up with all of you eventually.

In Memoriam: Brian Jacques

I noticed on Monday morning that both "Brian Jacques" and "Redwall" were trending on Twitter, and since I knew of no other reason for the terms to generate that much buzz, I feared the worst. My suspicions were soon confirmed. Brian Jacques, the author of the Redwall series, passed away at age 71 on February 5, 2011.

I owe a lot to Brian Jacques and his Redwall books, because they played a large role in making me who I am today. I suppose I was always destined to be a fantasy geek. I used to watch Power Rangers and Ninja Turtles and the X-Men cartoon, and my parents exposed me to Star Wars at an early age. But while my dad read The Hobbit and The Lord of the Rings to my brothers when they were in elementary school, he read more "girly" books to me, like Secret Garden and A Little Princess. To his credit, he did read me Watership Down, which between the rabbits, their made-up language, and their thrilling adventures, was my favorite book at the time.

But in third and fourth grade, my favorite genre was the survival genre--Island of the Blue Dolphins, Julie of the Wolves, Hatchet, and such. While I liked those books well enough, though, I didn't actually love to read. Reading was something I just did for school, or because my mother told me to do it. Redwall changed that.

One spring day when I was 10, I was looking for the next book to read. Knowing that I loved the animal adventures in Watership Down, my older brother handed me Mossflower, one of the books in the Redwall series (while it was written after the original book Redwall, it occurs earlier chronologically). It stars Martin the Warrior, a mouse who must travel to the mountain of the badger lord to repair his sword in order to free the good animals of Mossflower Woods from the oppression of the evil wildcat queen Tsarmina. It didn't take long before I was hooked, and over the next several years I devoured all of the books in the series that were out at the time (I kept up to date through 2003, reading a total of 16 of the novels; 21 have been released, and a 22nd is expected this year).

I'd been obsessed with otters since age 7, so I immediately loved the otter characters with their slings and sea-faring speech. The moles were adorable with their hard-to-understand rural accents, and the squirrels were great, leaping between trees with their bows and arrows. The food descriptions were amazing. Deeper'n'ever turnip'n'tater'n'beetroot pie, shrimp'n'hotroot soup, flans, trifles, strawberry cordial... I may not have known what a pasty was, but it sounded delicious. How I wished that I were an animal of Mossflower Woods who could enjoy that feast!

I loved the world of the Redwall books. I poured over the maps in the front of each book, trying to understand where Redwall Abbey in Mossflower Woods was in relation to other points of interest, such as the mountain Salamandastron, the Kingdom of Malkariss, and Marshank fortress. I would trace the paths that the heroes travelled, as each book would inevitably involve a hazardous journey over great distances. Each place had its own flavor with unique inhabitants, from the peaceful mice and other woodland creatures of Redwall to the jolly military hares and (less jolly) badger lord or lady of Salamandastron. Being transported to another world is one of my favorite things about the fantasy genre.

Most of all, I loved the heroics of the Redwall stories. Whether a trained warrior or a creature who had grown up as a dibbun in peaceful Redwall Abbey, the heroes would rise to the occasion to defend the innocent and to defeat evil and oppression. When Redwall was being attacked (as it so often was--the villains must have heard about their fabulous cuisine), every creature, young and old, defended the abbey and its citizens with their lives. Casualties were unavoidable, but the survivors honored the memories of those lost, knowing that they gave their lives for a good cause. The characters were lovable, the adventures were entertaining, the battles were exciting, and the trials and triumphs were moving.

The Redwall books were my favorite books all the way through middle school. My favorite of the series remains Martin the Warrior--the tale of Redwall's most legendary hero as he became the warrior who would one day liberate Mossflower Woods and help to found Redwall Abbey. But I also have a lot of love for Pearls of Lutra and its bow and arrow wielding otter heroine Grath. Some of the later books started to seem repetitive (I could solve most of the riddles immediately, as they tended to use the same tricks), and my memory blends them together a bit. But it didn't stop me from reading 16 of them.

The summer before my freshman year in high school, one of the optional books on the summer reading list was Sword of Shannara by Terry Brooks. It didn't have animals like my beloved Redwall, but it did have sword fights and a nice map in front, so it seemed a reasonable enough choice. I loved it, and I continued on to read a dozen from that series. That summer I also started the Harry Potter series, all of which I have now read, of course. By the time I started high school, I had completely embraced my fandom of the fantasy genre. J. R. R. Tolkien, Robert Jordan, Raymond Feist, and more were soon to follow. I even became a founding member and president of my high school's "Fantasy reader's guild". I was a geek and I was proud of it, and that fact continues to define me to this day.

The Redwall books guided me to the fantasy genre that has become such an important part of my life. But what's more, Mossflower was the first book that I couldn't put down, that I had to lock myself away in my room to finish, that I got mad at anyone who disturbed me reading it. Simply put, Brian Jacques' Redwall books are the books that made me love to read.

Two or three years ago, my mom went to a Brian Jacques reading and book signing at our local book store. She took three of our books along, so both of my brothers and I could get a signed copy (my younger brother picked up the series a few years after I did). When she got to the front of the line, she told him, "You are well loved in my family." He smiled and graciously said, "It warms my heart to hear that." I am sad that he is gone now, but his books have touched hundreds of thousands of lives in meaningful ways, and they will continue to do so in the future. I think that is pretty heroic.

Housemate in Antarctica photos: Scenery

Aside from having some amazing animals, Antarctica has breathtaking scenery.

A glacier out behind the station that people there like to hike up.


Scientists on a boat going by the glacier.


Sunset (some time around midnight) casts a gorgeous glow on the glacier.


Sunset lights the sky over the Antarctic waters and mountains.


I hope someday to be able to go to Antarctica and see its beautiful landscapes and remarkable animals myself. But it was really nice having a friend there. I was always impressed with the photos he sent me, and thanks to video chat I got to see some live video feed of penguins, seals, glaciers, and Antarctic sunsets. Video conferencing with the penguins. Almost like being there.

Well that's all for the Antarctica photos. I hope you enjoyed them as much as I did. Sorry again about my paranoid watermarks. I'm back from my cruise now, so I'll be playing catch up for a bit, then I'll return you to my regularly scheduled blog posts and tweeting. Not that I have a regular schedule or anything, but uh...yeah. See you around!

Housemate in Antarctica photos: Other animals

Though the Housemate took lots of penguin photos, there are of course lots of animals in Antarctica that aren't penguins.

The infamous leopard seal.

The Housemate told me that one time a huge leopard seal stuck its head up right next to a small boat he was on (see the next photo for what the boat probably looked like). He leaned in to get a better look, to the point that his co-worker had to pull him back because he was getting too close. But the Housemate said that it was so cute, just like a big puppy dog. I said, "Yeah, a puppy dog that could drag you down underwater and drown you." I was not pleased by the story, but it was kind of cute. As long as he promised not to get to close to the leopard seals again, even if they do look like giant puppies. It turns out there have been very few human deaths caused by leopard seals, but still, no reason to give them another opportunity.

Humpback whale!

It could just knock over the boat if it wanted.

This bird is a skua, which came up in my last post.


On Friday: Antarctica photos without animals as their subjects. There will be glaciers.

Housemate in Antarctica photos: Penguins!

As I've mentioned before on numerous occasions, my boyfriend has been in Antarctica since October doing research for his PhD. While I've missed him like crazy, one of the perks of him being there is that he sends me awesome photos he's taken. Sometimes he even takes his computer out so I can video chat with the penguins and seals around the station. So I get to live vicariously a little through him. He's taken some pretty excellent photos, so I figured I'd share a few of them with you.

(Apologies for the watermarks. I don't care so much about my own photos, but these aren't mine, and I'm finding myself a little paranoid about them. I tried my best to be both obnoxious and unobtrusive...yeah, it was kind of difficult.)

Even though they can be found many places throughout the southern hemisphere, you can't help associating penguins with Antarctica. Four species of penguins nest in Antarctica, but unfortunately the most famous of the four, the majestic emperor penguin, does not nest in the region where the Housemate is living. So here are the other three.

Chinstrap penguins, or "chinnies", are probably my favorite. Easily identifiable by the chinstrap-like marking under their chins.

From his stories, they seem pretty cheeky; one jumped up onto the small boat the Housemate was on, and stood there for about ten minutes checking them out. I think many of the penguins in Antarctica are like that, though--without hundreds of years of hunting by humans, the animals don't have the same fear of us that animals on other continents have learned.

Adelie penguins. There's a whole colony of them near the station, so he gets to see a lot of these guys.


And in December, their eggs hatched!

Baby penguin! The chicks were hard to get shots of, because the parents were very protective. They had to be--if they slipped up, a skua would be there to swoop in and take off with the baby for its breakfast :(

Gentoo penguins have the white marks above their eyes.


On Wednesday: animals in Antarctica that aren't penguins!

My college roommate's visit: Hanauma video

Yesterday, I told the story of the trip my college roommate and I took to Hanauma Bay. Here's the video footage I compiled from the snorkeling adventure. I forgot to show my friend how to take video on my camera, so all the footage is mine. Since I was mostly swimming at the surface of the water (the inner bay is very shallow), I get knocked around a bit by the waves, so it's not very steady. But you can see the "good spot" that we spent a lot of time at, a fish eating/playing with one of those "sea pen" seeds, a parrotfish crunching away at the algae on the reef (most of the video's sound is just annoying noise, but listen for the scraping sound!), and yes, the beautiful octopus cruising along the reef.



I hope you enjoyed my recent Hawaii photos. Next week, I'll have photos that the Housemate has taken in Antarctica; they will be posted on Monday, Wednesday, and Friday. First up: penguins!

My college roommate's visit: Hanauma

After finishing our hike up and down Diamond Head, we hurried over to Hanauma Bay. We got there maybe around 9:20, and there was already a long line. We didn't get in to see the required short video until after 10. But the wait went quickly enough, and it was all worth it. This was possibly the best snorkeling experience I've had in Hanauma Bay. Would have been even better if we'd seen a sea turtle, but we saw a lot of really great fish, and a wonderful octopus!

My friend and I were trading my camera back and forth, so I'm not sure who took some of these photos. But I'll give my best guesses.

I couldn't figure out what kind of fish this colorful guy is. It seems like it shouldn't be too hard, but I couldn't find it in my searches. Anyway, it's quite beautiful.

Photo by college roommate (positive)

Another one that I haven't identified yet.

Photo by college roommate (pretty sure)

This is a ringtail surgeonfish.

Photo by college roommate (or me...I'm really not sure here)

Another individual of the same species as above. I like that it's looking slightly towards the camera, but it's too bad I didn't get the whole fish.

Photo by me (positive)

OK, I have to share this story. My friend had the camera, I was just milling around a bit, looking at fish. Then I noticed a piece of trash floating in the water. I didn't really want to pick it up--if I were a guy wearing swim trunks with pockets, sure I'd stuff it in, but I had no pockets in my bikini. But the longer we stayed in the same spot, the guiltier I felt at not grabbing the trash, especially as the waves pushed me even closer to it. So I finally took it--it was the handle of a white plastic bag. I stuck it beneath the stretchy waistband of my bikini bottoms. Very stylish, I'm sure. But the next area of the reef that we swam to was spectacular. Tons of fish of many varieties, big and small. I felt like I was being rewarded for being a friend of the ocean.

I don't know what that long skinny floating thing is. I called them "sea pens" because they just float there looking like you're supposed to grab one and start scribbling. Fits quite nicely in my fingers, really. I think it must be a seed pod of some sort, floating to increase dispersal. You can also see some convict tangs here, among other fish.

Photo by me (sure)

The two cute yellow fish in the front are raccoon butterflyfish.

Photo by me (very sure)

These big guys are bluefin trevally.

Photo by me (very sure)

I think I'd caught glimpses of the big bluefin trevally before, but not anything like this, where a whole bunch of them just hung out right there.

Photo by me (very sure)

We stayed in that area for a very long time, just because more beautiful fish kept swimming by. We finally swam away to another area, then stood up (it was mostly very shallow where we were swimming) to discuss our next move. Then, we hear someone nearby say, "Look, there's an octopus over here!" More good ocean karma! My previous brief encounter with an octopus had taught me to hurry whenever there's an octopus sighting, so we swam right over to where the person was indicating.

But this one was in no particular hurry. It wasn't phased by our presence. It was just minding its own business. That purple fish, though, seemed to be even more interested in the octopus than we were. I'm not sure why. Maybe they were chatting. I love the way the octopus has its arms here, like a poofy gown.

Photo by me (positive)

Totally unconcerned by our presence. But see, that purple fish is still there! The colors on the octopus were really cool--it could change its colors, and even its texture a bit.

Photo by me (pretty sure)

We hung out with the octopus for a good long while. I'm still amazed it didn't swim away and hide from us. We finally decided to leave it, but before doing so, we called over another nearby group of people so they could appreciate it. And we made our way back toward the shore.

Tomorrow, see the video I took at Hanauma Bay. I got footage of the octopus going for a stroll, a big colorful parrotfish gnawing at the reef, and more!

My college roommate's visit: Diamond Head

We'd actually wanted to climb Diamond Head on Tuesday afternoon, but we got there only to find that the path is currently closed in the afternoons so they can do renovations on it.

We snapped this shot outside of the crater (on the side of the road), then went to spend our afternoon in Waikiki/Ala Moana (see yesterday's post).

Koko Head, from Diamond Head

The next morning, we got up early. It was her last day in Hawaii, and we had to do both Diamond Head and Hanauma Bay, both of which are best to do early, first thing in the morning. Unfortunately, we couldn't do both things first. Fortunately, the Diamond Head hike only takes one hour.

Looking out over the rim of the crater. I love the morning light on the water, and the rain visible on the left.


Usually I think of Diamond Head as being very dry and brown (look at the rim/ridges of the crater in the photos here). But the huge amount of rain we'd had recently made it surprisingly green.


The lighthouse by Diamond Head.


Well I had my photo of Diamond Head from Waikiki, now here's Waikiki from Diamond Head. You can see the pier that I took the photo from the day before, as well as the famed pink hotel of song (the Royal Hawaiian).

They paved paradise and put up a parking
With a pink hotel, a boutique, and a swinging hot spot

Tomorrow, see our photos from Hanauma Bay!

My college roommate's visit: Waikiki

For many tourists who come here, Hawaii is Waikiki. They paved paradise and put up a parking lot, after all--a parking lot for all the tourists and the tourist business. Hotels, boutiques, restaurants, bars, and ABC cheap souvenir stores on every block, it's an area locals generally try to avoid when possible (but there are reasons even for locals to go down there). Since it was my friend's first time in Hawaii, we had to make at least a quick stop to Waikiki.

Boogie boarders catch waves near a pier at Waikiki, with Diamond Head in the background.


We spent less than an hour in Waikiki. It's so crowded, and I prefer other beaches. We made our way to Ala Moana beach park, which isn't too far but is less crowded. The water is also very calm because of an offshore reef. It's a very pleasant place to swim.

I was impressed by the reflectivity of the building, which caught the setting sun so strongly that it reflected the light onto the water as if it were the setting sun itself.


The sunset cast lovely colors on the clouds.


My footprints, just for fun.


Tomorrow, see my photos from Diamond Head!

My college roommate's visit: Waimea Valley

I got very busy in December and didn't write very many blog posts, so the fact that my college roommate came to visit me in Honolulu was pretty glossed over. But she was here for five fun-filled days the week before Christmas. We hit up all my favorite restaurants (e.g. Spices, Shokudo, Legend Seafood, Kua 'Aina burgers, Kaka'ako Kitchen) and dessert spots (Waiola Shave Ice, Bubbies Ice Cream, and Dole Whip from Dole Plantation). And we went to many of the major Oahu tourist spots, as it was her first time in Hawaii.

We spent one day touring the North Shore, visiting Haleiwa, Turtle Bay, Waimea Valley, famous surf spots Pipeline, Sunset Beach, and Waimea Bay, and of course stopping at Dole Plantation for Dole Whip on the way home. The whole day was cloudy and most of it was rainy, but we made the most of it. My beach photos from that day were pretty drab (I have better photos of the same spots here, here, and here), but Waimea Valley, with its botanical gardens and waterfall, was still lovely in gray.


They had many varieties of hibiscus in the gardens. The dim light made most of my garden photos come out blurry, but this one managed to be clear, which made me really happy.


I don't remember what these flowers are called, but they're really cool. Soft, red, and about the size of a golf ball (maybe a little bigger? well the small ones were golf ball sized).


There's the waterfall up in the valley, going at full capacity. We'd had a LOT of rain recently (just the day prior, we got about 5 inches), so there was a lot of water flowing in that river with a lot of sediment, making the water brown.

In spite of the pool being small, it drops very quickly to 30 feet deep. There are lifeguards stationed there, offering free rentals of various flotation devices. We passed on the floaties and headed in, my camera strapped securely to my wrist (and clenched in my fist, just to be doubly safe, since I didn't have my floating wrist strap with me). The water was cold (by Hawaii standards...maybe 70F?), and the current was very strong due to the high volume flow. We had to work hard to swim to the waterfall--normal swimming only kept you in place!


But we fought the current and made it to the waterfall. We didn't go right underneath the waterfall, since we didn't quite feel like taking that kind of a pounding. But we did get underneath the fringes of the fall. It was very loud, which you just can't capture in a photo, and unfortunately I didn't think to take video at the time.

Admission to Waimea Valley is $13 for non-locals, $8 for locals, but I think it's worth it for the variety of interesting and beautiful plants and the well-maintained pool and waterfall. Maybe more worth it on a nice, sunny day, when the water isn't so brown and the current so strong. But we were still glad we went.

Tomorrow, see my beach photos from Waikiki and Ala Moana!